I'm using cupy and I want to know if there is any way to make the following calculation faster
import cupy as cp
cp.sum([cp.dot(var, cp.matmul(M, var)).item() for var in x])
Could parallelize with python built-in libraries but I don't know if it's the best (efficient) way to do it. My need arises from the fact that the above sum is done many times in another cycle for, moving through x
EDIT:
here x is an array with shape (m, n), so each var is a 1D array of length n, by other hand M is a matrix with shape (n,n).
Related
I am generating a series of Gaussian arrays given a x vector of length (1400), and arrays for the sigma, center, amplitude (amp), all with length (100). I thought the best way to speed this up would be to use numpy and list comprehension:
g = np.sum([(amp[i]*np.exp(-0.5*(x - (center[i]))**2/(sigma[i])**2)) for i in range(len(center))],axis=0)
Each row is a gaussian along a vector x, and then I sum the columns into a single array of length x.
But this doesn't seem to speed things up at all. I think there is a faster way to do this while avoiding the for loop but I can't quite figure out how.
You should use vectorized computation instead of comprehension so the loops are all performed at c speed.
In order to do so you have to reshape x to be a column vector. For example you could do x = x.reshape((1400,1)).
Then you can operate directly on the arrays, like this:
v=(amp*np.exp(-0.5*(x - (center))**2/(sigma)**2
Then you obtain an array of shape (1400,100) which you can sum up to a vector by np.sum(v, axe=1)
You should try to vectorize all the operations. IMHO the most efficient to first converts your input data to numpy arrays (if they were plain Python lists) and then let numpy process the computations:
np_amp = np.array(amp)
np_center = np.array(center)
np_sigma = np.array(sigma)
g = np.sum((np_amp*np.exp(-0.5*(x - (np_center))**2/(np_sigma)**2)),axis=0)
I have a matrix X and I need to write a function, which calculate a trace of matrix .
I wrote a next script:
import numpy as np
def test(matrix):
return (np.dot(matrix, matrix.T)).trace()
np.random.seed(42)
matrix = np.random.uniform(size=(1000, 1))
print(test(matrix))
It works fine on small matrix, but when I try to calculate on large matrix (for example on matrix with shape (50000, 1)), it gives me a memory error.
I tried to find a solution to the problem in other questions on the site, but nothing helped me. I would be grateful for any advice!
The number you're trying to compute is just the sum of the squares of all entries of X. Sum the squares instead of computing a giant matrix product full of entries you don't want:
return (X**2).sum()
Or ravel the matrix and use dot, which is probably faster for contiguous X:
raveled = X.ravel()
return raveled.dot(raveled)
Actually, ravel is probably faster for non-contiguous X, too - even when ravel needs to copy, it's not doing more allocation than (X**2).sum().
I have a simple problem for Numpy: I have 3d coordinates and I want to compute the overlap between two distinct configurations with the following function
def Overlap(rt, r0,a):
s=0
for i in range(len(rt)):
s+=(( pl.norm(r0[i]-rt ,axis=1) <=a).astype('int')).sum()
return s`
Where rt and r0 represent two m by 3 tables, the configurations.
Practically, it computes the distance between a vector in the first configuration and any other vector in the second, checks for a threshold value a, and returns the total sum after a loop over all the positions. Is there a smart way to avoid the explicit for loop? I have the feeling that the complexity cannot really be changed, but there is maybe a way to avoid the slowness of the native for construct.
How about the following:
from scipy.spatial.distance import cdist
import numpy as np
overlap = np.sum(cdist(rt, r0) <= a)
When m is 1000 on my machine, this is about 9x faster. It's much faster for small arrays
import numpy
from scipy.spatial.distance import pdist
X = numpy.zeros(50000,25)
C = pdist(X, 'euclidian')
I want to find:
And then numpy gives error : Array is too big.
I think problem is about array size of C. Pdist cannot creates (50000,50000) array. I dont know why numpy restricts? I can run same code in matlab. How can i run this code using array?
And also ,i found possible duplication but their array-matrix size too big.
Is it possible to create a 1million x 1 million matrix using numpy?
Very large matrices using Python and NumPy
first thing there are a couple of typos in your code. It's:
X = numpy.zeros((50000,25)) # it's a tuple going in
C = pdist(X, 'euclidean') # euclidean with an e
of course it does not matter for the question.
The Euclidean pdist is just a call for numpy.linalg.norm (http://docs.scipy.org/doc/numpy/reference/generated/numpy.linalg.norm.html). It's a very general function. If it does not work in your case due to memory constraints you can always create something yourself. Two 50000 length vectors do not take that much memory and this can make one pairwise comparison:
np.sqrt(np.sum(np.square(X[0])) + np.sum(np.square(X[1])))
And then you only need to loop through the whole thing.
Hope it helps,
P
Is there a way to use numpy.linalg.det or numpy.linalg.inv on an nx3x3 array (a line in a multiband image), for example? Right now I am doing something like:
det = numpy.array([numpy.linalg.det(i) for i in X])
but surely there is a more efficient way. Of course, I could use map:
det = numpy.array(map(numpy.linalg.det, X))
Any other more direct way?
I'm pretty sure there is no substantially more efficient way than what you have. You can save some memory by first creating an empty array for the results and writing all results directly to that array:
res = numpy.empty_like(X)
for i, A in enumerate(X):
res[i] = numpy.linalg.inv(A)
This won't be any faster, though -- it will only use less memory.
a "normal" determinant is only defined for a matrix (dimension=2), so if that's what you want i don't see another way.
if you really want to compute the determinant of a cube then you could try to implement one of the ways described here:
http://en.wikipedia.org/wiki/Hyperdeterminant
notice that it is not necessarily the same value as the one you're currently computing.
New answer to an old question: Since version 1.8.0, numpy supports evaluating a batch of 2D matrices. For a batch of MxM matrices, the input and output now looks like:
linalg.det(a)
Compute the determinant of an array.
Parameters a(…, M, M) array_like
Input array to compute determinants for.
Returns det(…) array_like
Determinant of a.
Note the ellipsis. There can be multiple "batch dimensions", where for example you can evaluate a determinants on a meshgrid.
https://numpy.org/doc/stable/reference/generated/numpy.linalg.det.html
https://numpy.org/doc/stable/reference/generated/numpy.linalg.inv.html